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AIP conference proceedings

Spin ordering in the one-dimensional Kondo lattice and Double-exchange Models

Daniel J. García

Published Jan 1, 2003• 0 citations
Publisher

Abstract

We study the spin ordering of localized quantum spins interacting with itinerant electrons via antiferromagnetic (Kondo model) or ferromagnetic (Hund coupling) exchange interactions in the one‐dimensional lattice models. In the case of ferromagnetic coupling we also include a super‐exchange interaction between the localized spins. Using the Density Matrix Renormalization Group (DMRG) we show, for both models, the existence of new magnetic phases with spin ordering consisting of ferromagnetic islands coupled antiferromagnetically.

DOI
10.1063/1.1639598

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We study the spin ordering of localized quantum spins interacting with itinerant electrons via antiferromagnetic (Kondo model) or ferromagnetic (Hund coupling) exchange interactions in the one‐dimensional lattice models. In the case of ferromagnetic coupling we also include a super‐exchange interaction between the localized spins. Using the Density Matrix Renormalization Group (DMRG) we show, for both models, the existence of new magnetic phases with spin ordering consisting of ferromagnetic islands coupled antiferromagnetically.
We study numerically the one-dimensional Kondo and Hund lattices consisting of localized spins interacting antiferromagnetically or ferromagnetically with the itinerant electrons, respectively. Using the density-matrix renormalization group we find, for both models and in the small coupling regime, the existence of new magnetic phases where the local spins order forming ferromagnetic islands coupled antiferromagnetically. Furthermore, by increasing the interaction parameter |J| we find that this order evolves toward the ferromagnetic regime through a spiral-like phase with longer characteristic wavelengths. These results shed new light on the zero temperature magnetic phase diagram for these models.
We investigate the magnetic order and related strongly correlated effects in a one-dimensional Ising-Kondo lattice with transverse field. This model is the anisotropic limit of the conventional isotropic Kondo lattice model, in the sense that the itinerant electrons interact with the localized magnetic moments via only longitudinal Kondo exchange. Adopting the numerical density-matrix renormalization group method, we map out the ground-state phase diagram in various parameter spaces. Depending on the Kondo coupling and filling number, three distinct phases, including a metallic paramagnetic, a metallic ferromagnetic, and a gapped spin-density wave phase, are obtained. The spin-density wave is characterized by an ordering wave vector, which coincides with the nesting wave vector of the Fermi surface. This makes the corresponding magnetic transition a spin analog of the Peierls transition occurring in the one-dimensional metal. Moreover, by analyzing the momentum distribution function and charge correlation function, the conduction electrons are shown to behave like free spinless fermions in the ferromagnetic phase. We finally discuss the effect of the repulsive Hubbard interaction between conduction electrons. Our paper enriches the Kondo physics and deepens the current understanding of the heavy fermion compounds.
Using a non-Abelian density matrix renormalization group method we determine the phase diagram of the Kondo lattice model in one dimension, by directly measuring the magnetization of the ground state. This allowed us to discover a second ferromagnetic phase missed in previous approaches. The phase transitions are found to be continuous. The spin-spin correlation function is studied in detail, and we determine in which regions the large and small Fermi surfaces dominate. The importance of double-exchange ordering and its competition with Kondo singlet formation is emphasized in understanding the complexity of the model.
We consider a one-dimensional Hund lattice model where a conducting band is coupled with localized spins s = 1/2 interacting antiferromagnetically, with coupling constant J , and investigate the ground state phase diagram as a function of both the exchange coupling J and the band filling, n . From spin structure factor measurements we found different evolving magnetic orderings in the ground state related to the particle distribution in the systems, although no charge density waves are formed, as found from density-density correlation function measurements. We study the quasiparticle formation and phase separation using the density-matrix renormalization group method, which is a highly efficient method to investigate quasi-one-dimensional strongly correlated systems.
We study higher-spin ($S\ensuremath{\ge}1$) generalization of the one-dimensional Kondo-Heisenberg model, in which the local spin-SSS moments of the Kondo-lattice model interact with each other via the antiferromagnetic Heisenberg interaction (JH{J}_{\text{H}}JH​), by analytical and numerical methods. The strong-coupling (i.e., large Kondo coupling) expansion maps out an insulating phase at half-filling whose magnetic correlation depends on the parity of 2S2S2S as well as a ferromagnetic metallic phase which dominates the strong-coupling region at generic fillings. Then, we carried out the density-matrix renormalization-group simulations for S=1S=1S=1 to closely investigate the phase structure at large but finite Kondo coupling. At half-filling, the Kondo coupling and JH{J}_{\text{H}}JH​ do not compete and the insulating spin-gapless phase is stable, while the competition of the two leads to a stepwise collapse of the strong-coupling ferromagnetism via an intervening dimerized insulating phase with power-law spin correlation at quarter-filling.
We analyze superconducting correlations in the one-dimensional Kondo lattice models with Ising anisotropy under transverse magnetic fields, using the density matrix renormalization group. For the spin-1/2 local spin model, the Ising anisotropy is introduced by the ferromagnetic Ising interaction between the local spins, while for the spin-1 model, it is taken by the single-ion anisotropy. The magnetic properties under the transverse fields for the spin-1/2 model are very similar to those for the spin-1 model [K. Suzuki and K. Hattori, J. Phys. Soc. Jpn. 88, 024707 (2019).]. For the superconducting correlations, we analyze various Cooper pairs within nearest-neighbor pairs including composite ones between the local spins and the electrons. We find that, for the spin-1/2 model, the superconducting correlations are highly enhanced in the Tomonaga-Luttinger liquid state near the Kondo-plateau phase, where the conduction electrons and the local spins are strongly coupled with a finite spin gap for the Ising axis. This is a clear contrast to the model under the longitudinal magnetic fields, where there are no noticeable superconducting correlations. Competitions between the transverse magnetic field and the Kondo singlet formation lead to this enhanced superconducting correlations. For the spin-1 model, the single-ion anisotropy suppresses the superconducting correlation and there is no noticeable enhancement. We also examine the large Kondo exchange coupling limit. For the moderate ferromagnetic Ising interaction between the local spins, we find that another type of superconducting correlation is enhanced inside the ferromagnetic phase. We discuss a possible relation between our results and reentrant superconductivity in U-based ferromagnetic superconductors under transverse magnetic fields.